2. Parametric Modeling...performed a case study on the leaning Capital Gate Tower in Abu Dhabi. Kim and Hong (2011) estimated the pro-gressive collapse potential of irregular buildings

Title: Comparative Evaluation of Structural Systems for Tilted Tall Buildings

Author: Kyoung Sun Moon, School of Architecture, Yale University

Subject: Structural Engineering

Keywords: OutriggersStructure

Publication Date: 2014

Original Publication: International Journal of High-Rise Buildings Volume 3 Number 2

Paper Type: 1. Book chapter/Part chapter2. Journal paper3. Conference proceeding4. Unpublished conference paper5. Magazine article6. Unpublished

© Council on Tall Buildings and Urban Habitat / Kyoung Sun Moon

ctbuh.org/papers

http://ctbuh.org/papers

International Journal of High-Rise Buildings

June 2014, Vol 3, No 2, 89-98International Journal of

High-Rise Buildingswww.ctbuh-korea.org/ijhrb/index.php

Comparative Evaluation of Structural Systems for

Tilted Tall Buildings

Kyoung Sun Moon†

Yale University School of Architecture, New Haven, CT 06511, USA

Abstract

Employing tilted forms in tall buildings is a relatively new architectural phenomenon, as are the cases with the Gate ofEurope Towers in Madrid and the Veer Towers in Las Vegas. This paper studies structural system design options for tilted tallbuildings and their performances. Tilted tall buildings are designed with various structural systems, such as braced tubes,diagrids and outrigger systems, and their structural performances are studied. Structural design of today’s tall buildings builtwith higher strength materials is generally governed by lateral stiffness. Tilted towers are deformed laterally not only by lateralloads but also by dead and live loads due to their eccentricity. The impact of tilting tall buildings on the gravity and lateralload resisting systems is studied. Comparative evaluation of structural systems for tilted tall buildings is presented.

Keywords: Tilted tall buildings, Diagrids, Braced tubes, Outrigger structures

1. Introduction

Buildings have traditionally been constructed vertically,

orthogonal to the ground. When a building is found to be

tilted, it is typically an indication of some serious pro-

blems occurred to the building. The leaning Tower of

Pisa (Fig. 1) is a famous example of tilted buildings due

to differential settlements. Today, however, tilted build-

ings are intentionally designed and built to produce more

dramatic architecture, as are the cases with the Gate of

Europe Towers of 1996 in Madrid (Fig. 2) designed by

Philip Johnson/John Burgee, Veer Towers of 2010 in Las

Vegas by Helmut Jahn, and the design of the Signature

Towers in Dubai by Zaha Hadid (Fig. 3).

Tall buildings carry very large gravity and lateral loads.

Therefore, structural impacts of tilting tall buildings are

significant, and more careful studies are required for the

design of tilted tall buildings. Though not uncommon

these days, design and construction of tilted tall buildings

are a still very recent architectural phenomenon, and only

a limited amount of related research has been conducted.

Scott et al. (2007) presented general design considera-

tions for tall buildings of complex geometries, including

leaning towers, with examples of the Songdo Northeast

Asia Trade Tower and the Fiera Milano. Erakovic et al.

(2010) studied the structural design and performance of

the tilted Veer Towers in Las Vegas. Schofield (2012)

performed a case study on the leaning Capital Gate Tower

in Abu Dhabi. Kim and Hong (2011) estimated the pro-

gressive collapse potential of irregular buildings includ-

ing tilted buildings of 30 stories. Kim and Jung (2012)

presented progressive collapse resisting capacities of

tilted tall buildings of 36 stories.

Structural design of tall buildings is generally governed

by lateral stiffness (Connor, 2003; Ali & Moon, 2007).

While a considerable amount of research has been carried

out by many researchers and engineers about structural

systems for conventional prismatic form tall buildings,

impacts of tilting tall building structures on lateral stiff-

ness have not been much investigated. This paper studies

†Corresponding author: Kyoung Sun MoonTel: +1-203-436-8983; Fax: +1-203-432-7175E-mail: [email protected]

Figure 1. Leaning Tower of Pisa (Courtesy of StephenStaples).

90 Kyoung Sun Moon | International Journal of High-Rise Buildings

structural system design options for tilted tall buildings with various structural systems and evaluates their lateral performances comparatively.

Unlike vertical tall buildings, tilted tall buildings are

subjected to large initial lateral deformations and locali-

zed stresses due to their eccentricity. This paper also dis-

cusses these important structural issues. Though tilted

forms have emerged as a new form of tall building archi-

tecture, research on this subject is still very rare and more

studies are needed. This paper systematically studies and

evaluates structural systems for tilted tall buildings.

2. Parametric Modeling

In order to illustrate the concepts underlying the struc-

tural behavior of tilted tall buildings, sixty-story towers of

various angles of tilt are designed with three different

structural systems prevalently used for today’s tall build-

ings, i.e., braced tubes, diagrids and outrigger structures.

Structural steel is used for the design of all three struc-

tural systems in this study, though reinforced concrete or

composite structures are also commonly used in real

world. Each system’s structural performance depending

on various angles of tilt is investigated comparatively

based primarily on lateral stiffness. Parametric structural

models are generated using appropriate computer prog-

rams such as Rhino/Grasshopper to investigate the impact

of varying angle of tilting. The models are exported to

structural engineering software, SAP 2000, for design,

analysis and comparative studies. Fig. 4 shows example

Figure 2. Gate of Europe Towers in Madrid (Courtesy ofAntony Wood, CTBUH).

Figure 3. Signature Towers (Courtesy of Zaha HadidArchitects).

Figure 4. 3D structural models of variously tilted tall buildings generated using Rhino/Grasshopper and SAP 2000.

Comparative Evaluation of Structural Systems for Tilted Tall Buildings 391

3D structural models of tilted tall buildings generated

using Rhino/Grasshopper and SAP 2000.

The SEI/ASCE Minimum Design Loads for Buildings

and Other Structures is used to establish the wind load.

The structures are assumed to be in Chicago and within

category III, which implies that there is a substantial

hazard to human life in the event of failure. Based on the

code, the basic wind speed is 40.2 meters per second (90

miles per hour). One percent damping is assumed for the

calculation of the gust effect factor. Considering the fact

that the structural design of tall buildings is generally

governed by lateral stiffness, preliminary member sizes

for the straight tower are generated first to satisfy the

maximum lateral displacement requirement of a five hun-

dredth of the building height. The maximum allowable

displacement of tall buildings, one of the most important

stiffness-based design parameters, is typically in the nei-

ghborhood of this value (Kowalczyk et al., 1995).

3. Tilted Braced Tubes

Braced tubes, with their superior structural efficiency,

have often been used for tall buildings, such as the John

Hancock Center in Chicago, Renaissance Tower in Dallas

and 780 Third Avenue in New York to name a few. This

section investigates structural performance of braced

tubes employed for tilted tall buildings. A 60-story tall

rectangular box form straight tall building is designed

with the braced tube system first, and the building is tilted

at four different angles as shown in Fig. 5. Case 1.1 is the

straight braced tube tower. The building’s typical plan

dimensions are 36×36 meters with an 18×18-meter core

at the center, which produces a floor depth of 9 meters

between the building façades and the core perimeter

walls. Typical story heights are 3.9 meters. The braced

tube system on the building perimeter is designed to carry

the entire lateral loads, and the 18×18-meter building core

is designed to carry only gravity loads, in order to esti-

mate the impact of different angles of tilting on the per-

formance of the perimeter braced tube.

Fig. 6, with simplified section drawings of the tilted

braced tubes, clearly explains the relationship between

the vertical building core and the tilted perimeter braced

tube for each tilted case. Case 1.2 is a tilted case with no

floor offset. While the 18×18-meter gravity core is kept

vertical within the tilted perimeter braced tube, the build-

ing is tilted to its maximum angle of 4 degrees. Therefore,

on the left side of the building as seen in Fig. 6, the dis-

tance between the exterior façade and the core perimeter

wall reduces from 18 meters on the ground to 0 meter at

the top. On the right side, this distance increases from 0

meter on the ground to 18 meters at the top. Though this

specific configuration produces some architectural issues

regarding the space use as the distance between the exte-

rior façade and the core perimeter wall nears 0 meter, this

study is focused more on structural aspects and assumes

architectural issues can be reasonably resolved in the end.

The tilted form of this case is similar to that of the Gate

of Europe Towers in Madrid shown in Fig. 2 or the Veer

Towers in Las Vegas.

Case 1.3, 1.4 and 1.5 are tilted braced tube towers with

floor offsets of 12, 16 and 20 stories at both the top and

bottom, resulting in tilted angles of 7, 9 and 13 degrees,

respectively. Tilted forms of these cases are similar to

those of the Signature Towers shown in Fig. 3. In these

cases, the 18×18-meter gravity cores are still kept vertical

within the perimeter braced tube structures.

The preliminary structural design is performed based

on the stiffness-based design methodology developed for

braced tubes by Moon (2010). A braced tube building is

Figure 5. 60-story tilted braced tube structures of various tilted angles (elevation view).


modeled as a cantilever beam, and subdivided longitudi-

nally into modules according to the repetitive pattern.

Each module is defined by a single level of diagonals that

extend over multiple stories. Fig. 7 illustrates a 10-story

braced tube module. Member sizes for the braced tube

modules of a tall building can be computed using Eqs. (1)

and (2) (Moon, 2010).

(1)

(2)

Ad is area of each diagonal; Ac is area of each column;

V is shear force; M is moment; E is modulus of elasticity

of steel; θ is angle of diagonal member; γ is transverse

shear strain; χ is curvature; Nc,f is number of columns on

each flange frame; δc is contribution of web columns for

bending rigidity; B is building width in the direction of

applied force.

In order to study the structural performances of braced

tube systems of various tilted angles comparatively, the

member sizes used for the straight tower are also used for

the tilted towers for preliminary designs. The final design

will obviously necessitate deferent sizes for each case to

a certain degree. Some necessary adjustments are still

made for the interior gravity column sizes because the

tributary areas in the tilted zones change due to tilting the

tower at different angles. However, the influence of the

interior gravity columns on the tower’s lateral stiffness is

negligible.

Fig. 8 and Table 1 summarize the maximum lateral dis-

placements of the tilted braced tubes in the direction pa-

rallel to the direction of tilting, when the wind load is

applied also in the same direction. Lateral stiffness of the

tilted braced tubes against wind loads is very similar to

that of the straight braced tube regardless of the changes

of the tilted angle between 0 and 13 degrees. However,

Ad

V

4E θ θγsin2

cos

---------------------------------=

Ac

2M

Nc f, δc+( )B2Eχ

----------------------------------=

Figure 6. 60-story tilted braced tube structures (section view).

Figure 7. 10-story braced tube module.Figure 8. Maximum lateral displacements of the tiltedbraced tube structures shown in Fig. 5.


initial lateral displacements of the tilted braced tubes due

to gravity loads are significant. This gravity-induced late-

ral displacement, which is even larger than the wind-

induced displacement in most cases, becomes greater as

the angle of tilting increases. The combined maximum la-

teral displacement of the braced tube is increased from

44.9 cm of Case 1.1 to 105.6 cm of Case 1.5. It should

be noted, however, that gravity-induced lateral displace-

ments of tilted tall buildings can be managed substantially

during construction if planned carefully.

4. Tilted Diagrids

With their structural efficiency and powerful expres-

sion, diagrid structures have widely been used for recent

tall buildings, such as the 30 St. Mary Axe in London,

Hearst Tower in New York and Guangzhou International

Financial Center in Guangzhou. This section investigates

structural performance of diagrids employed for tilted tall

buildings. The 60-story buildings are now designed with

the diagrid structural system. Fig. 9 shows the straight

diagrid structure and its four different tilted versions. The

important dimensions and tilted angles of the diagrid

structures are the same as those of the braced tube struc-

tures studied in the previous section. Design conditions

including applied loads are also the same as before. The

major difference is that the perimeter braced tubes studied

in the previous section are replaced with diagrids.

The preliminary structural design is performed first for

the straight diagrids shown in Case 2.1 of Fig. 9, based on

the stiffness-based design methodology developed by

Moon et al. (2007). A diagrid structure is modeled as a

cantilever beam, and subdivided longitudinally into mo-

dules according to the repetitive diagonal pattern. Each

module is defined by a single level of diagonals that

extend over multiple stories. Fig. 10 illustrates an 8-story

diagrid module. Member sizes for the diagrid modules

can be computed based on the required lateral stiffness

using Eqs. (3) and (4) (Moon et al., 2007).

(3)

(4)

Ad,w is area of each diagonal on the web; Ad,f is area of each diagonal on the flange; V is shear force; M is moment; E is modulus of elasticity of steel; θ is angle of diagonal member; γ is transverse shear strain; χ is cur-

vature; B is building width; Ld is length of diagonal; Nd,w

Ad w,

VLd

2Nd w, Ehγ θ2

cos

------------------------------------=

Ad f,

2MLd

Nd f, δd+( )B2Eχh θ

2sin

---------------------------------------------------=

Table 1. Maximum lateral displacements of the tilted braced tube structures

Tilted Angle (degrees)Gravity-Induced Max. Lat-

eral Displacement (cm)Wind-Induced Max. Lateral

Displacement (cm)Combined Max. Lateral

Displacement (cm)

Straight 0 0.0 44.9 44.9

0 Fl Offset 4 42.2 43.8 86.0

12 Fl Offset 7 53.7 44.4 98.1

16 Fl Offset 9 58.1 44.5 102.6

20 Fl Offset 13 59.7 45.9 105.6

Figure 9. 60-story tilted diagrid structures of various tilted angles (elevation view).


is number of diagonals on each web plane; Nd,f is number

of diagonals on each flange plane; δd is contribution of

web diagonals for bending rigidity.

In order to study the structural performances of diagrid

systems of various tilted angles comparatively, the mem-

ber sizes used for the straight diagrids are also used for

the tilted diagrids for preliminary designs. Fig. 11 and

Table 2 summarize the maximum lateral displacements of

the tilted diagrid towers in the direction parallel to the

direction of tilting, when the wind load is also applied in

the same direction. The performance of the diagrids is

very similar to that of the braced tubes previously studied.

Lateral stiffness of the tilted diagrids against wind loads

is very similar to that of the straight diagrids regardless of

the changes of the tilted angle between 0 and 13 degrees.

However, initial lateral displacements of the tilted dia-

grids due to gravity loads are significant. This gravity-

induced lateral displacement, which is even larger than

the wind-induced displacement in most cases, becomes

greater as the angle of tilting increases.

5. Tilted Outrigger Structures

Outrigger structures are another prevalently used struc-

tural system for today’s tall buildings. Notable examples include the Jin Mao Building in Shanghai, Taipei 101 in Taipei, International Commerce Center in Hong Kong to name a few. The 60-story tilted buildings are now desi-

gned with the outrigger system. Fig. 12 shows the straight outrigger structure and its four different tilted versions. The important dimensions and tilted angles of the outrig-

ger structures are the same as those of the braced tube or diagrid structures studied in the previous sections. Other design conditions, including the applied wind loads, are also the same as before. The major differences are that the primary lateral load resisting system is changed to the outrigger system. Consequently, lateral load resisting bra-

ced frames are employed for the core structures of the outrigger systems, instead of the gravity core structures without bracings, employed for the previously studied braced tubes and diagrids. For the straight outrigger tower shown in Case 3.1 of Fig. 12, the outrigger trusses, which connect the braced core and perimeter mega-columns, are placed at a third and two-thirds heights of the building. The locations of the outrigger trusses are adjusted for en-

hanced constructability depending on the offset locations of different cases as can be seen in Fig. 12.

Structural design is performed for Case 3.1 first to

satisfy the maximum lateral displacement requirement of

a five hundredth of the building height. Based on prelimi-

nary studies on the optimal lateral stiffness distribution

between the braced core and perimeter mega-columns,

40% of the required bending stiffness is provided by the

braced core and the rest by the mega-columns, connected

to the braced core through the outrigger trusses. The steel

braced core is designed based on Eqs. (1) and (2) presen-

ted earlier. The member sizes for the braced core and

mega-columns of the straight outrigger structure are also

used for the tilted outrigger structures, for preliminary

designs. The outrigger truss member sizes are adjusted

according to the length of the trusses. Overall, similar

Figure 10. An 8-story diagrid module.

Table 2. Maximum lateral displacements of the tilted diagrid structures




Displacement (cm)

Straight 0 0.0 48.3 48.3

0 Fl Offset 4 39.3 47.4 86.7

12 Fl Offset 7 55.1 46.2 101.3

16 Fl Offset 9 59.4 46.3 105.7

20 Fl Offset 13 62.5 46.5 109.0

Figure 11. Maximum lateral displacements of the tilteddiagrid structures shown in Fig. 9.


amount of structural materials are used for the five cases

studied.

Fig. 13 and Table 3 summarize the maximum lateral

displacements of the tilted outrigger structures in the

direction parallel to the direction of tilting, when the wind

load is also applied in the same direction. The perfor-

mance of the tilted outrigger structures is different from

that of the tilted braced tubes or diagrids. Lateral stiffness

of the tilted outrigger structures against wind loads is

greater than that of the straight outrigger structure. The

tilted outrigger structures configured as shown in Fig. 12

carry lateral loads more effectively because tilting the

tower results in triangulation of the major structural com-

ponents - the braced core, mega-columns and outrigger

trusses. As the angle of tilting increases from 0 to 13 de-

grees, the geometry of the triangles, formed by the major

structural components, becomes more effective to resist

the wind load, and, consequently, the wind-induced maxi-

mum lateral displacement of the outrigger structure dec-

reases. Fig. 14 shows wind-induced lateral displacements

of Cases 3.1, 3.2 and 3.5.

As in the cases with the braced tubes or diagrids, the

tilted outrigger structures are also substantially deformed

initially due to dead and live loads. This gravity-induced

lateral deformation increases as the angle of tilting

increases. However, gravity-induced lateral displace-

ments of tilted outrigger structures are smaller than those

of the tilted braced tubes or diagrids, again, due to the tri-

angulation of the major structural components. Because

of the increased lateral stiffness against wind loads and

relatively small gravity-induced deformation, the total

lateral displacements of the tilted outrigger structures are

smaller than those of the tilted braced tubes or diagrids.

The maximum lateral displacements of the braced tube,

Figure 12. 60-story tilted outrigger structures of various tilted angles (section view).

Table 3. Maximum lateral displacements of the tilted outrigger structures




Displacement (cm)

Straight 0 0.0 47.8 47.8

0 Fl Offset 4 38.6 37.9 76.5

12 Fl Offset 7 42.7 34.6 77.3

16 Fl Offset 9 52.0 33.6 85.6

20 Fl Offset 13 53.9 34.6 88.5

Figure 13. Maximum lateral displacements of the tiltedoutrigger structures shown in Fig. 12.


diagrid and outrigger structures due to the combined gra-

vity and wind loads are 105.6, 109.0 and 88.5 cm res-

pectively, with a tilted angle of 13 degrees.

6. Comparison between the Systems

The performance of a tilted tall building is dependent

upon its structural system and angle of tilting. Fig. 15

summarizes wind-induced maximum lateral displacements

of the tilted braced tubes, diagrids and outrigger struc-

tures shown in Figs. 5, 9 and 12, respectively, when the

wind load is applied in the direction of tilting. The lateral

stiffness of the braced tube and diagrid systems is not

substantially influenced by the angle of tilting between 0

and 13 degrees studied here. The lateral stiffness of the

outrigger system is increased by tilting the tower due to

the triangulation of the major structural components - the

braced core, mega-columns and outrigger trusses. Fig. 16

summarizes gravity-induced maximum lateral displace-

ments of the tilted braced tubes, diagrids and outrigger

structures. While gravity-induced lateral displacements

increase as the angle of tilting increases in all the three

structural systems, the gravity-induced displacements of

the outrigger structures are relatively small because of the

triangulation of the major structural components. Fig. 17

summarizes the total maximum lateral displacements of

the tilted braced tubes, diagrids and outrigger structures.

Figure 14. Wind-induced lateral displacements of Cases3.1, 3.2 and 3.5 shown in Fig. 12.

Figure 15. Wind-induced maximum lateral displacementsof the tilted braced tubes, diagrids and outrigger structuresshown in Figs. 5, 9 and 12.

Figure 16. Gravity-induced maximum lateral displacementsof the tilted braced tubes, diagrids and outrigger structuresshown in Figs. 5, 9 and 12.

Figure 17. Total maximum lateral displacements of thetilted braced tubes, diagrids and outrigger structuresshown in Figs. 5, 9 and 12.


The studies presented thus far have been about tilted

tall buildings subjected to wind loads applied in the direc-

tion of tilting. When wind load is applied in the direction

perpendicular to the direction of tilting, the tilted tower is

not only deformed laterally but also twisted. As the angle

of tilting increases, the rate of twisting also increases. The

right image of Fig. 18 shows the deformed shape, seen

from above, of the 60-story braced tube of Case 1.5 sub-

jected to the code-defined wind load in the direction per-

pendicular to the direction of tilting. In this case, the

tower’s maximum lateral displacement of the upper left

corner is 49.3 cm, while that of the upper right corner is

51.4 cm at the top due to the twisting action. The maxi-

mum twisted angle is 0.03 degrees at the top in this case.

As a comparison, the left image of Fig. 18 shows the de-

formed shape with no twisting action of the same struc-

ture subjected to the wind load in the direction of tilting.

The maximum twisted angle of the tilted diagrid structure

of Case 2.5 is 0.02 degrees, which is similar to the twisted

angle of the braced tube. The maximum twisted angle of

the tilted outrigger structure of Case 3.5 is 0.07 degrees.

This angle is much larger than the angles observed from

the same studies with the tilted braced tube and diagrid

structures because torsional stiffness of the outrigger struc-

ture is much smaller than that of the perimeter tube type

structures with diagonals, such as braced tubes and dia-

grids.

7. Strength Consideration for Tilted Tall Buildings

Structural design of tall buildings is generally governed

by lateral stiffness rather than strength. This study thus far

has focused on the lateral stiffness of the structural sys-

tems for tilted tall buildings. Tilted towers are subjected

to much larger localized stresses than conventional ver-

Figure 18. Deformed shapes of the 60-story tilted braced tube of Case 1.5 seen from above with wind in the directionparallel to the direction of tilting (left) and in the direction perpendicular to the direction of tilting (right).

Figure 19. Axial member forces of the tilted braced tubes subjected to dead, live and wind loads.


tical towers. As examples, Fig. 19 shows axial member

forces of the vertical and two tilted braced tube structures

(Cases 1.1, 1.2 and 1.5 of Fig. 5) subjected to combined

dead, live and wind loads. Much larger compressive and

tensile member forces are developed in the tilted braced

tubes than in the straight braced tube.

Tensile forces developed in tall buildings due to wind

loads are often cancelled by compressive forces caused

by dead and live loads (Smith and Coull, 1991; Taranath,

1998). In the tilted braced tubes studied here, however,

substantial tensile forces are developed in perimeter co-

lumns and bracings due to the eccentricity. More careful

studies are required for the design and construction of the

connections of these members.

8. Conclusions

This paper presented lateral stiffness-based structural

performance of contemporary structural systems employed

for tilted tall buildings. The lateral stiffness of a tilted

tower is dependent upon the structural system and angle

of tilting. Compared to the perimeter tube type structures,

such as braced tubes and diagrids, the outrigger system

provides greater lateral stiffness when used for tilted

towers because of the triangulation of the major structural

components - the braced core, outrigger trusses and mega-

columns - caused by tilting the tower. Torsional stiffness

is greater in the perimeter tube type structures than in the

outrigger structures. Thus, the tube type tilted structures

are less twisted against wind loads applied in the direc-

tion perpendicular to the direction of tilting.

Tilted towers are significantly deformed due to dead

and live loads. These gravity-induced deformations can

be managed substantially through careful construction

planning. As the angle of tilting increases, very large lo-

calized stresses are developed in tilted tall buildings due

to the eccentricity. Though structural design of tall buil-

dings is generally governed by lateral stiffness, careful

studies on satisfying strength requirements are also essen-

tial for tilted tall buildings. Large tensile forces, not very

often found in conventional vertical tall buildings, can be

developed in tilted tall buildings. Careful design studies

on the connections of the tensile members of tilted tall

buildings are required.

Many studies have been carried out for tall buildings of

conventional forms. However, complex-shaped tall buil-

dings, the structural behavior and design of which are

more complicated, have not been much investigated. This

paper presented comparative evaluation of structural sys-

tems for tilted tall buildings based on static analysis. Fur-

ther research, such as studying on bi-axially tilted towers and dynamic analysis of tilted towers with various angles of tilt, is required to more comprehensively understand the structural behavior of tilted tall buildings. With preva-

lent emergence of complex-shaped tall buildings, includ-

ing tilted towers, in the major cities throughout the

world, more rigorous research is necessary to construct

higher quality built environments.

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Documents

2. Parametric Modeling...performed a case study on the leaning Capital Gate Tower in Abu Dhabi. Kim and Hong (2011) estimated the pro-gressive collapse potential of irregular buildings